Dynamic Fracture of Concrete and other Heterogeneous Materials.

Closed form solutions have been developed for wave propagation problems in materials which have a constitutive equation with strain softening SS. These solutions have been useful in assessing the performance of finite element programs and in examining the validity of SS models from physical grounds. The salient characteristics of these wave propagation solutions with SS is that the strain softening localizes into a domain of one-dimension smaller than the space of the problem for example, in a one-dimensional wave propagation problem, the strain softening localizes to a single point where strain softening is first initiated. Furthermore, if the stress goes to zero as the strain increases in the SS discontinuity is introduced in the displacement. A more serious shortcoming is the absence of energy dissipation in the SS part of the continuum. This absence is due to the extreme localization of the SS phenomenon. Since strain-softening models are usually intended to model dissipative processes such as microcracking or crushing of material, the absence of dissipation is quite troublesome. To overcome this drawback of the SS continuum model, a nonlocal theory was examined. In a non-local theory, the stresses depend on an average of the strain in a volume about the point at which the stress is being computed. In this type of theory, the localization which is characteristic of strain softening solutions can be limited and a finite amount of energy dissipation which is relatively insensitive to element size, can be achieved. Keywords Concrete Structures Failures Size effects.